Encyclopedia of Microtonal Music Theory

7/12-tone, seven-twelfth-tone

[Joe Monzo]

Calculated as the 72nd root of 27 -- 72√27, or 2(7/72) -- an irrational proportion with the approximate ratio of 1 : 1.069711846, and an interval size of exactly 116 2/3 cents. It is the size of 7 degrees in the 72-edo (or 72-tET) scale, and gives a good approximation to both the just intonation diatonic semitone (ratio 16:15 = 2,3,5-monzo [4 -1, -1>) and the pythagorean chromatic semitone or apotome (ratio 2187:2048 = 2,3-monzo [-11 7,>).

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